Earlier today, I presented three challenging symmetry puzzles for you to solve. Let’s revisit these puzzles and take a closer look at the solutions.
1. Triangle Twins:
The first puzzle features two ’30-60-90′ triangles that share a side length. Your task is to rearrange these triangles without any overlaps to create a shape with mirror symmetry. This means that a line can divide the shape into two identical halves. Can you find both solutions?
Solution: One way to solve this puzzle is by cutting out the triangles and physically rearranging them until you achieve mirror symmetry.
2. Tetromino Triplets:
For the Tetris enthusiasts out there, the second puzzle involves three L-shaped tetrominos. Your goal is to rearrange these shapes without overlaps so that the combined shape exhibits a line of mirror symmetry. There are two ways to achieve this – one without flipping any shapes and one with flipping.
Solution: You can try cutting out the tetrominos and manipulating them on a surface to find the solutions.
3. Triomino Quintuplets:
Lastly, the third puzzle introduces five L-triominos. Your challenge is to rearrange these shapes without overlaps to create a combined shape with a line of mirror symmetry. The line of symmetry should be either parallel or perpendicular to all the edges of the triominos.
Solution: Experiment with cutting out the triominos and arranging them to create a symmetrical shape.
These puzzles were provided by Donald Bell, a former director of the National Engineering Laboratory, who has a passion for polyominoes. If you’re interested in learning more about polyominoes, you can listen to a talk he gave on the subject.
I hope you enjoyed tackling these symmetry puzzles. If you have any puzzle suggestions or would like to share your solutions, feel free to email me. I’ll be back in two weeks with more brain teasers for you to enjoy.
Remember, the best way to solve these puzzles is by getting hands-on and physically manipulating the shapes. Have fun puzzling!
